Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-4x-8y &= 2 \\ 2x+y &= 2\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $2x = -y+2$ Divide both sides by $2$ to isolate $x$ $x = {-\dfrac{1}{2}y + 1}$ Substitute this expression for $x$ in the first equation. $-4({-\dfrac{1}{2}y + 1}) - 8y = 2$ $2y - 4 - 8y = 2$ Simplify by combining terms, then solve for $y$ $-6y - 4 = 2$ $-6y = 6$ $y = -1$ Substitute $-1$ for $y$ in the top equation. $-4x-8( -1) = 2$ $-4x+8 = 2$ $-4x = -6$ $x = \dfrac{3}{2}$ The solution is $\enspace x = \dfrac{3}{2}, \enspace y = -1$.